Australia · Year 12 · Practice Sheet 21

1. 1.

   Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 2.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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2. 2.

   A force of 18 N moves an object 10 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A 29 kg object moves at 13 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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4. 4.

   Find the population standard deviation of: 8, 14, 16, 7, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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5. 5.

   A population of 4,400 grows 2% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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6. 6.

   Solve using the quadratic formula: x² − 2x − 24 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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7. 7.

   An object with initial velocity 3 m/s accelerates at 4.1 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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8. 8.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 4 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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9. 9.

   Two masses 8,900 kg and 720 kg are 7 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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10. 10.

    $2,600 is invested at 6% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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11. 11.

    A device runs at 239 V drawing 7.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A force of 37 N moves an object 29 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    Find the gravitational potential energy of a 15 kg object raised 23 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Find the momentum of a 49 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A triangle has sides a = 19 cm and b = 6 cm with an included angle C = 60°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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16. 16.

    In a triangle, a = 14, b = 7 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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17. 17.

    A population of 3,500 grows 3% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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18. 18.

    A body starts at 6 m/s and accelerates at 4.8 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A force of 102 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    An object with initial velocity 3 m/s accelerates at 4.7 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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